Oren Miller -- with wife Beth Blauer -- was an inspirational figure for many dad bloggers.

Editor’s Note: Kelly Wallace is CNN’s digital correspondent and editor-at-large covering family, career and life. Read her other columns and follow her reports at CNN Parents and on Twitter.

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Two years ago, a dad blogger called attention to the "Amazon Mom" program

After his death, dads are urging the retail giant to change the name to "Amazon Family"

The petition drive has gotten more than 4,800 signatures

CNN  — 

Many years ago, a colleague told me how frustrated her husband was by “Amazon Mom,” a special membership program offered by the retail giant that provides discounts, recommendations and other information to help parents during the crazy toddler years.

In bold print, the company says the program is “open to anyone, whether you’re a mom, dad, grandparent, or caretaker.”

But still it is called “Amazon Mom,” irking my colleague’s husband to no end since he was the one ordering the majority of diapers and other products for their babies.

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My friend’s husband was not alone. A petition created a few years ago calls on Amazon to change the name of the program from “Amazon Mom” to “Amazon Family.”

But the drive didn’t get much traction.

That changed after the recent death of a beloved dad blogger, Oren Miller, who created a Facebook group for dad bloggers in 2012 that has grown to more than 1,000 members.

In 2013, Miller called on men and women to sign the petition to get Amazon to change the name of the program.

“Why did Amazon bother changing the name of its parenting program when the program started in the UK? What made them realize they couldn’t get away with calling it ‘Amazon Mom,’ and why do they get away with it here?” Miller wrote.

“Someone actually started a petition to change the name to ‘Amazon Family’ in the US, and so far it has less than 100 signatures. Why is that? Why are we OK with letting England be more progressive than we are here when it comes to fatherhood? They have a queen! They are ruled by a freakin’ queen! We can do better than that!” he wrote.

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I had the pleasure of interviewing Miller for a story last year on whether modern dads get enough credit. The 42-year-old stay-at-home father of two, who fought perceptions of fathers as nothing more than babysitters in essays on his blog, was diagnosed with lung cancer in 2014.

Miller, of Owings Mills, Maryland, died Saturday.

Now, members of the dad blogging community are rallying in his honor, trying to step up the pressure on the Internet powerhouse to finally change the name of its program and get with the times.

Mike Heenan, a stay-at-home father of two in Northern California and founder of the blog At-Home Dad Matters, never got to meet Miller but says that when Miller welcomed him into his community of dad bloggers, it changed his life.

“He got me writing again, inspired me to publish, to contribute, to tell my story … to be a better dad for my daughters.”

Heenan, like several other dad bloggers, took to Twitter using the #AmazonFamilyUS hashtag to call for Amazon to make the change.

“The push for inclusivity in the parenting arena has been well received by many a brand in the past few years and, like Oren, many of us think the change to ‘Amazon Family’ is a no-brainer,” Heenan said.

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Buzz Bishop, a father of two in Calgary, Alberta, and founder of the blog Dad Camp, points out how Amazon calls its program “Amazon Family” in Germany, Japan, Austria, France and Canada as well as the United Kingdom.

“So why is it called ‘Amazon Mom’ in America?” Bishop wrote in a blog post.

“We are continuing a cause that was once championed by the creator of the Dad Bloggers Facebook group, Oren Miller,” wrote Bishop.

“In his name, we want to finish the job.”

The petition has gotten over 4,800 signatures.

Amazon has not commented on the movement.

In the meantime, Miller’s supporters won’t stop pushing.

I hope they never do.

Do you think Amazon should re-name its “Amazon Mom” program “Amazon Family”? Share your thoughts with Kelly Wallace on Twitter or CNN Living on Facebook.